We seek to build new models of neural processing that parallel the explicit, neural space, consisting of spikes, synapses, neurons, and neural circuits, and an implicit probability space that implements Bayesian learning and inference in an underlying statistical model.
As a starting point, we propose to view cortical neurons as accumulating evidence over time about a particular hypothesis regarding the state of the environment, the body or the task. This hypothesis could be the presence or absence of a preferred stimulus in this neuron's receptive field, the appropriateness of a particular movement, or a more abstract component in a combinatorial code, a "hidden variable" describing an underlying statistical structure in sensory data. However, rather than computing directly an answer to their questions (is the hypothesis true or false?), neurons compute and communicate to other neurons their certainty about this hypothesis being true or false.
Because the state of these variables are likely to change over time, and the main difficulty is to correctly detect these changes, spikes, and more generally neural activity, signals the occurrence of new probabilistic evidence that could be not predicted from previous spikes fired by the same neuron pr other neurons in the same population. In support of this hypothesis, neural responses to salient and unpredictable events, or to errors of predictions, tend to be much stronger than responses to static, boring stimuli. In particular, our current research suggests that a neuron involved in such probabilistic computations would have the dynamics of a leaky integrate and fire neuron with adaptation (spike-based, synaptic) and plasticity (spike time dependant) close to those observed in cortical neurons.

Addiction presents a complex behavioral process whose causes can be postulated on a multiplicity of levels, from molecular and pharmacological to cognitive. Computational approaches to addiction should bridge the neural with the behavioural/cognitive phenomena. Our approach is multi-level . We are striving to synthesize the effects of the drug on the receptor level, neural circuit level and decision making level in order to disentangle the roles of the primary rewarding and hedonic processes of the drug and the opponent processes in the progression from use to addiction.
We focus on nicotine addiction with the overall hypothesis being that self-administration of nicotine results from an abnormally biased learning at the level of the reward and action selection neural circuits. This initial self-administration, when prolonged, leads to the persistent addiction, lasting possibly the life time of the animal/person. The model is developed to reflect the neuroadaptations induced by the drug (nicotine) at the circuit and receptor level, and to marry those with computational models of reinforcement learning. In the initial stage of the project we have proposed a minimal model of nicotine addiction under a simple choice paradigm. We frame the model in terms of actor-critic framework, proposing specific anatomical substrates for both and suggesting a differential drug action. We take into account the changes to neuronal activity induced directly by the drug, in short- and long- term. Such neuroadaptation then lead to pathological action learning, resulting in addictive behavior. The minimal model accounts for a number of experimental findings. This minimal model forms an initial framework for a development of a more comprehensive computational theory of drug addiction. We plan to extend the model to address more complex behavioral situations and to tease apart how the various learning processes are affected by the drug (e.g. learning of reward vs. learning of actions) leading to habitual drug taking. We also plan to consider the role of the prefrontal cortex, in particular executive cognitive control by such over the reward- and action-selection circuits, in addiction.

The capacity of the nervous system to update a motor command by a comparison between the sensory feedback and the efferent copy is well established (Wolpert et al, 1995). This requires the existence of an internal model for the state of the body, predicted from the efferent motor commands, and corrected by the sensory feedback. The relative strength of the feedback and the efferent copy ideally depends on the sensory and motor noise, and can be computed using a Kalman filter.
In collaboration with Pierre Baraduc in the Institute of Cognitive Science in Lyon, France, we are currently testing the prediction of these models for the control of eye movements and arm movements, particularly whether the gains attributed to the visual feedback movements and sequences of movements is adjusted according to the motor noise. In particular we seek new methods to measure the subject's uncertainty about their on-line effector location estimate during the movement, as opposed to only at the end of the movement.

A current project of mine is concerned with how synaptic input is integrated in active dendritic trees. The classic picture of summation of synaptic input in passive dendritic cables has been strongly challenged over the last decade. Many experimental studies have shown that dendrites are endowed with a wide variety of voltage-dependent ion channels. Particularly interesting is that inputs to the dendrites are able to locally generate spikes. These dendritic spikes can propagate to the soma and lead to a somatic action potential. Obviously these properties greatly influence the integrative properties of the neuron. In a collaboration with Boris Gutkin and Mate Lengyel I'm currently studying how synaptic inputs to active dendrites interact and what kind of computations can be performed.

Several behavioral experiments suggest that the nervous system use an internal model of the dynamics of the body to implement a close approximation to a Bayesian filter. This filter can be used to perform a variety of tasks near optimally such as predicting the sensory consequence of motor action, integrating sensory and body posture signals, and computing motor commands. We propose that the neural implementation of this Bayesian filter involves recurrent basis function networks with attractor dynamics, a kind of architecture that can be readily mapped onto cortical circuits. In such networks, the tuning curves to variables such as arm velocity are remarkably non invariant in the sense that the amplitude and width of the tuning curves of a given neuron can vary greatly depending on other variables such as the position of the arm, or the reliability of the sensory feedback. This property could explain some puzzling properties of tuning curves in the motor and premotor cortex, and leads to several new predictions.

A striking analogy exists between the Bayesian networks (graphical models) that are used in machine learning, and recurrent neural networks, that also contain nodes (neurons or neural population) links (axons and synapses) and multidirectional propagation of messages (spikes in the case to neural network, beliefs in the case of Bayesian network). In particular, we can make a parallel between the factorization of the joint probability distribution, the nodes in the graphical model that represents the statistical structure of the perceptual and motor environment, and the modular structure of the brain that implement this graphical model.
Our major objective is neurons as building blocks in a new theory of cortical computations, where neural networks implement an underlying, hierarchical statistical model, and where the multidirectional flow of information within cortical networks is interpreted as a propagation of beliefs allowing each neuron to compute the probability of its hypothesis to be true given evidence received in the entire brain. More generally, we propose to show that networks of biophysical spiking neurons approximate Bayesian inference by a local message passing algorithm called belief propagation in a corresponding Bayesian network.

For the analysis of single neurons we take the minimal modeling approach, which attempts to construct the simplest structural model for explaining an observed phenomenon, using mechanisms based on known physiological processes. The goal of this approach is to create models that display non-trivial behavior, provide experimentally testable predictions, and are amenable to analysis. A central interest of mine is developing mathematical methods that produce minimal models. In other words models that are mathematically tractable, and yet reflect the very heart of the neural mechanism that underlies the neural or cognitive phenomenon. This, slightly abstracted and mathematical approach can produce not only individual models, but also a theory with a wider brush stroke, and hopefully allow one to unify previously disparate data.
For example, the transition from evoked to repetitive firing in many conductance-based neural models is produced by a specific dynamical mechanism: the saddle-node bifurcation, seen when the associated phase-space diagrams are studied in the context of non-linear dynamical systems. This is known as "Type I" membrane excitability, as defined by A. Hogdkin in his seminal work from 1948. By using normal form reduction a simple canonical one-equation model for this dynamical class can be derived and used to make qualitative statements generic to the whole class. Thus by studying this canonical model we are studying behavior of a wide class of excitable membranes and thus - neurons.
Neurons spike generating dynamics can be characterized by its Phase Response Function - a measure of how timing of individual spikes is shifted by weak transient inputs (e.g. single EPSP and/or IPSP). We are building upon the canonical theory of spike generation to predict the shapes of PRCs in cortical neurons and link these with other standard measures of neural response.
We have derived an extended reduced model that includes slow adaptation (spike frequency adaptation). We showed how such adaptation can shape the bifurcations underlying the generation of action potentials. Such adaptive processes, linked with a family of slow potassium currents, are under exquisite control of neuromdulators such as achetylcholine and dopamen. We are currently studying experimentally the effect of such modulators on the structure of the spike generating dynamics in cortical neurons.
We have identified that neurons can respond to transient excitatory inputs either with high precision, independent of the spike emission probability, or with variable (arbitrary) delays. In the second case the distribution of spike times depends on the spike emission probability. We are now identifying the mechanisms underlying this and studying its consequences for coding.
We are further exploring the consequence of spike generating dynamics and adaptation on the computation performed by the neurons in the context of Bayesian information processing.

Dopaminergic Modulation of Working Memory Circuit. Upper: General Model Network Diagram Lower: Transfer Function of the BG Units - DA induces bistability. Gruber et al 2006.

We have studied the mechanisms of working memory formation. This is the kind of memory where information is held actively on-line for use in generating cognition-guided action and behavior. Neurons in several cortical areas, and particularly in the dorsolateral prefrontal cortex of primates show sustained activity that is a neural representation of the working memory trace. We are exploring the dynamical mechanisms underlying this activity, focusing on the structure of spiking in such circuits and the influence of neuromodulation.
The underlying theoretical models for this activity are the so-called 'bump' attractors or sustained foci of activity that are spatially and temporally stable. We have considered the relationship between the structure of spike-timing within a bump attractor and its stability. We have shown an "inhibitory" effect of synchronizing excitation, that is sustained activity stops when the active neurons are synchronized. This is independent of the neuronal model used and also independent of recurrent inhibition. We have suggested that this could be an efficient way to update the representations in working memory.
We are studying the influence of noise on the stability and the onset of sustained activity in spiking neural circuits. We have shown that random excitatory synaptic inputs can disrupt sustained activity in a simple, purely excitatory circuit. We are presently analyzing the mechanism for this and studying the consequences for neural phenomena as up-down states.
We have studied bump formation and stability in networks with patchy long-range lateral connections: excitatory "lattices". We have also found that patchy connections can play a role in sustaining multiple bumps by proving that these stabilize the coexistence of multiple bumps, hence traces of multiple memories.
We have studied the influence of basal ganglia on the stability of bump attractors. We have specifically examined the role of dopamine in modulating the relative interactions between the prefrontal cortex and the basal ganglia, suggesting that dopaminergic modulation enables contextual control of memory store access.
We have started to consider what happens when multiple bumps of activity are placed onto a recurrent network with lateral inhibition. Initial simulations show, in agreement with previous work, that such multiple 'memories' interact and can only exist in a small number of relative spatial configurations.